# One-Shot Operational Quantum Resource Theory

## TL;DR

This paper develops a unified framework for one-shot quantum resource manipulation, establishing bounds on resource conversion efficiency using various entropy-based measures across multiple resource theories.

## Contribution

It introduces a general approach to quantify one-shot resource conversion efficiency applicable to diverse quantum resource theories.

## Key findings

- Derived bounds on optimal resource formation and distillation rates.
- Unified framework encompassing entanglement, coherence, and other resources.
- Operational meanings for resource measures in one-shot scenarios.

## Abstract

A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max/min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. Our results encompass a wide class of resource theories via the theory-dependent coefficients we introduce, and the discussions are solidified by important examples, such as entanglement, coherence, superposition, magic states, asymmetry, and thermal non-equilibrium.